We show that a Noetherian ring
R is locally quasi-unmixed if and only if for every prime ideal P ∈Â∗(I),
ht(P) = l(IRP). The analytic spread of an e.p.f., l(f) is also defined and many of the
known results for the integral closures of powers of an ideal are proven for the weak
integral closures of the ideals in a strong e.p.f. Several characterizations
are given of when a Noetherian ring R is locally quasi-unmixed in terms
of analytic spreads and integral closure of ideals. Several applications of
these equivalences are given by showing when certain prime ideals are in
Â∗(f).
